(3) Land stability index [31,39] (*LSI*):

One of the most significant effects of land-use conflicts on regional spatial patterns is the fragmentation of landscape patches, which presents as a changing process from a continuously varying structure to a mosaic of patches that tend to be complex, heterogeneous and discontinuous. The conservation of many biological species requires large areas of natural habitat. With the fragmentation of the landscape and the shrinking area of patches, the environment suitable for living organisms is decreasing, which will directly affect the reproduction, dispersal, migration and conservation of species. Therefore, landscape fragmentation is one of the main reasons for the loss of biodiversity and decline of ecosystem stability.

Patch density (*PD*), a commonly used landscape index, was used to represent landscape fragmentation and reflect the degree of land stability. A higher *PD* value indicates a higher degree of landscape fragmentation, poorer land stability, and the more intense the conflict in a unit area [35,44].

Therefore, the *LSI* can be expressed as the reverse of the *PD* and was calculated as follows (Formula (4)):

$$LSI = 1 - PD\tag{4}$$

The *PD* was calculated as follows (Formula (5)):

$$PD = \frac{n\_i}{A} \tag{5}$$

In this formula, *ni* refers to the number of landscape patches of space type *i*, and *A* refers to the total area of the spatial unit. To simplify and standardize the calculations, the index values obtained were standardized to 0~1.

A 500 m × 500 m grid was selected as the measurement unit based on the research scale, the total amount of data, and the landscape patch situation. Based on the results of existing research [44], the conflict values were classified into four grades: stable and controlled [0,0.4], basically controlled (0.4,0.6], basically uncontrolled (0.6,0.8] and severely uncontrolled (0.8,1.0].

#### *3.2. Land-Use Conflict Spatial Analysis Methods*

#### 3.2.1. Spatial Autocorrelation Analysis

Spatial autocorrelation analysis reflects the correlation between the values of a variable in a space and the surrounding space and can also be used to determine whether there is autocorrelation between the different spaces. To study the spatial distribution of spatial units with different degrees of land-use conflict, this research used GeoDa 1.14 software to establish spatial weights based on adjacency relationships and used the global spatial autocorrelation index *Moran's I* and the local spatial autocorrelation index LISA [45–47] to measure the spatial autocorrelation characteristics of land-use conflict in Lin'an District.

(1) Global spatial autocorrelation index. The global spatial autocorrelation index *Moran's I* was calculated as follows (Formula (6)):

$$Norm's\ I = \frac{n}{\sum\_{i=1}^{n}\sum\_{j=1}^{n}\mathcal{W}\_{ij}} \times \frac{\sum\_{i=1}^{n}\sum\_{j=1}^{n}\mathcal{W}\_{lj}(\mathbf{x}\_{i}-\overline{\mathbf{x}})(\mathbf{x}\_{j}-\overline{\mathbf{x}})}{\sum\_{i=1}^{n}(\mathbf{x}\_{i}-\overline{\mathbf{x}})^{2}}\tag{6}$$

In this formula, *n* refers to the total number of sample points of variable *x*; *xi* and *xj* refer to the values of variable *x* at spatial locations *i* and *j,* respectively; *x* refers to the average values of *n* location attribute values; and *Wij* refers to the elements of the binary spatial weight matrix *W* in general cross-product statistics, which reflect the location similarity of spatial units.

*Moran's I* reflects the degree of similarity in the comprehensive index of land use conflict in units around a space. Its value range is [–1,1]; values of (0,1] indicate positive spatial autocorrelation, 0 indicates no spatial autocorrelation, and values of [–1,0) indicate negative spatial autocorrelation [48]. Based on this analysis, the Monte Carlo simulation method was used to calculate the *Z* value and the *P* value for further testing.

(2) Local spatial autocorrelation index. The local spatial autocorrelation index *LISA* was calculated as follows (Formula (7)):

$$LISA \ = \frac{n(\mathbf{x}\_i - \overline{\mathbf{x}})}{\sum\_{j} (\mathbf{x}\_i - \overline{\mathbf{x}})^2} \sum\_{j} \mathcal{W}\_{ij} (\mathbf{x}\_i - \overline{\mathbf{x}}) \tag{7}$$

When the *LISA* index value is positive, the similarity values around a unit are clustered in space; when the *LISA* index value is negative, non-similar values around the unit are clustered in space.

#### 3.2.2. Terrain Gradient-Based Analysis

Topographic factors have a key influence on a land-use pattern. Lin'an District is a typical hilly area with large topographic undulations, scarce arable land resources, and tense human–land relations. The characteristics of land use conflicts vary significantly with changes in topographic features. Therefore, the slope factor was chosen to explore the topographic gradient characteristics of land-use conflicts in Lin'an District.

The reclassification module of ArcGIS was used to classify the slope index to quantitatively explore the land-use conflict characteristics in Lin'an District. With reference to the current classification standards and the actual surface morphology of the study area, the slope reclassification of Lin'an District was divided into three categories, namely, low slope [0◦, 6◦], medium slope (6◦, 25◦] and high slope (25◦, 90◦]. After that, the spatial distribution of the land-use conflict degree in 2008, 2013 and 2018 were overlaid with the slope classification to explore the characteristics of land-use conflicts under different slope conditions in Lin'an District.
